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GCF of 2 and 6

GCF of 2 and 6 is the largest possible number that divides 2 and 6 exactly without any remainder. The factors of 2 and 6 are 1, 2 and 1, 2, 3, 6 respectively. There are 3 commonly used methods to find the GCF of 2 and 6 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 2 and 6
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 2 and 6?

Answer: GCF of 2 and 6 is 2.

Explanation:

The GCF of two non-zero integers, x(2) and y(6), is the greatest positive integer m(2) that divides both x(2) and y(6) without any remainder.

Methods to Find GCF of 2 and 6

Let's look at the different methods for finding the GCF of 2 and 6.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

GCF of 2 and 6 by Long Division

GCF of 2 and 6 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 6 (larger number) by 2 (smaller number).
Step 2: Since the remainder = 0, the divisor (2) is the GCF of 2 and 6.

The corresponding divisor (2) is the GCF of 2 and 6.

GCF of 2 and 6 by Prime Factorization

Prime factorization of 2 and 6 is (2) and (2 × 3) respectively. As visible, 2 and 6 have only one common prime factor i.e. 2. Hence, the GCF of 2 and 6 is 2.

GCF of 2 and 6 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 6 and Y = 2

GCF(6, 2) = GCF(2, 6 mod 2) = GCF(2, 0)
GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 2 and 6 is 2.

☛ Also Check:

GCF of 2 and 6 Examples

Example 1: Find the greatest number that divides 2 and 6 exactly.

Solution:

The greatest number that divides 2 and 6 exactly is their greatest common factor, i.e. GCF of 2 and 6.
⇒ Factors of 2 and 6:
- Factors of 2 = 1, 2
- Factors of 6 = 1, 2, 3, 6
Therefore, the GCF of 2 and 6 is 2.
Example 2: For two numbers, GCF = 2 and LCM = 6. If one number is 6, find the other number.

Solution:

Given: GCF (z, 6) = 2 and LCM (z, 6) = 6
∵ GCF × LCM = 6 × (z)
⇒ z = (GCF × LCM)/6
⇒ z = (2 × 6)/6
⇒ z = 2
Therefore, the other number is 2.
Example 3: The product of two numbers is 12. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 12
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 12/2
Therefore, the LCM is 6.

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FAQs on GCF of 2 and 6

What is the GCF of 2 and 6?

The GCF of 2 and 6 is 2. To calculate the GCF of 2 and 6, we need to factor each number (factors of 2 = 1, 2; factors of 6 = 1, 2, 3, 6) and choose the greatest factor that exactly divides both 2 and 6, i.e., 2.

How to Find the GCF of 2 and 6 by Long Division Method?

To find the GCF of 2, 6 using long division method, 6 is divided by 2. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

How to Find the GCF of 2 and 6 by Prime Factorization?

To find the GCF of 2 and 6, we will find the prime factorization of the given numbers, i.e. 2 = 2; 6 = 2 × 3.
⇒ Since 2 is the only common prime factor of 2 and 6. Hence, GCF (2, 6) = 2.
☛ What is a Prime Number?

If the GCF of 6 and 2 is 2, Find its LCM.

GCF(6, 2) × LCM(6, 2) = 6 × 2
Since the GCF of 6 and 2 = 2
⇒ 2 × LCM(6, 2) = 12
Therefore, LCM = 6
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 2, 6?

The following equation can be used to express the relation between Least Common Multiple and GCF of 2 and 6, i.e. GCF × LCM = 2 × 6.

What are the Methods to Find GCF of 2 and 6?

There are three commonly used methods to find the GCF of 2 and 6.

By Prime Factorization
By Listing Common Factors
By Long Division

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